Eigenvectors Of Correlation Matrices Research Articles

Integral Cryptanalysis Using Algebraic Transition Matrices

In this work we introduce algebraic transition matrices as the basis for a new approach to integral cryptanalysis that unifies monomial trails (Hu et al., Asiacrypt 2020) and parity sets (Boura and Canteaut, Crypto 2016). Algebraic transition matrices allow for the computation of the algebraic normal form of a primitive based on the algebraic normal forms of its components by means of wellunderstood operations from linear algebra. The theory of algebraic transition matrices leads to better insight into the relation between integral properties of F and F−1. In addition, we show that the link between invariants and eigenvectors of correlation matrices (Beyne, Asiacrypt 2018) carries over to algebraic transition matrices. Finally, algebraic transition matrices suggest a generalized definition of integral properties that subsumes previous notions such as extended division properties (Lambin, Derbez and Fouque, DCC 2020). On the practical side, a new algorithm is described to search for these generalized properties and applied to Present, resulting in new properties. The algorithm can be instantiated with any existing automated search method for integral cryptanalysis.

Block Cipher Invariants as Eigenvectors of Correlation Matrices

A new approach to invariant subspaces and nonlinear invariants is developed. This results in both theoretical insights and practical attacks on block ciphers. It is shown that, with minor modifications to some of the round constants, Midori-64 has a nonlinear invariant with $$2^{96} + 2^{64}$$ corresponding weak keys. Furthermore, this invariant corresponds to a linear hull with maximal correlation. By combining the new invariant with integral cryptanalysis, a practical key-recovery attack on ten rounds of unmodified Midori-64 is obtained. The attack works for $$2^{96}$$ weak keys and irrespective of the choice of round constants. The data complexity is $$1.25 \cdot 2^{21}$$ chosen plaintexts, and the computational cost is dominated by $$2^{56}$$ block cipher calls. The validity of the attack is verified by means of experiments.

Classification of radio pulsars using the principle-components method

The principle-components method is used as a basis to analyze the distributions of known radio pulsars in spaces of eigenvectors of correlation matrices for various samples of pulsars and classification parameters (from 4 to 11 parameters characterizing the physical and kinematic properties of the objects). Pulsars with periods P 0) Galactic latitudes do not differ; i.e., there is no anisotropy in the motions in these two directions perpendicular to the Galactic plane, or in the corresponding distributions of the pulsar parameters.

Influence in canonical variates analysis

Results from the perturbation theory of the symmetric eigenproblem are used to develop influence functions of eigenvalues and eigenvectors in canonical variates analysis. Influence functions of Mahalanobis' squared distances among the group centroids are also derived. Three sample versions of these functions are described and some properties are noted. The same methodology is used to determine influence functions of eigenvalues and eigenvectors of correlation matrices.